The upconversion noise we generate in dark fringe when shaking the benches (for WE elogs: 20207 20434, for the NE elogs: 20257 20258 20381 20400 20405 20424 20435 20487) looks well reproduced by this simple model:
Noise(t) = G * sin(2*2pi/lambda * d(t) * g)
This model is justified theoretically by S.Braccini computations in http://wwwcascina.virgo.infn.it/collmeetings/presentations/2006/2006-02/DetectorMeeting/Braccini_Feb06_Bench_Diffusion.ppt
The model uses:
- the horizontal bench displacement "d(t)" which is provided by the episensor. In particular the bench displacement that counts is that along the z beam direction (using the orthogonal horizontal direction, and the vertical one do not reproduce as nicely the measured noise).
- a parameter "g", which makes a small adjustment to the bench displacement. It is tuned in order to best match the relative amplitude of the upconversion peaks. The "g" parameter varies between 1.2 and 1.4, and it accounts for the fact that the scattering object moves 20% to 40% more than the bench surface plane.
- another parameter "G", which is an overall scale factor and is adjusted to match the amplitude of the noise in the h-calibrated dark fringe.
For each bench, the simulation parameters are tuned on the shaking data. Figures 1 and 2 show one example for WE and NE.
The "G" parameter is actually the most important one. It gives a measurement of the "coupling" of the bench displacement to the dark fringe, being somehow proportional to the amount of back-scattered light from the bench into the ITF.
We measure these values of "G", in units of 10^-20 (assume a 50% error on these values):
WE, before the mitigation works: 9.0
WE, after the works: 2.4
NE, before the mitigation works: 2.5
NE, after the works: 0.9, 1.4, 0.9 (*)
(*) NE was re-measured on April 21, April 29, and May 6.
The tuned simulation is then used to project the noise produced by the quiet bench displacement. Figures 3 and 4 are for WE, before and after the works. Figures 5 and 6 are for the NE.
In Figures 4 and 6, three different quiet spectra are projected to give an idea of how much the present noise changes because of variations of seismic noise of the bench.
Some conclusions:
- At WE the noise reduced by a factor of about 4. It is now close to the Virgo design, but still a factor 2 above it around 20Hz (Figure 4).
- At NE the noise reduced by a factor of about 2. The remaining coupling is lower than at WE, meaning that the residual diffused light is less than at the WEB. The noise projection for this bench is shown in Figure 6 (I chose the worst measured G=1.4e-20, in order to be conservative). The residual noise is a bit worst than at WE. This is because the NE bench moves at the 20Hz resonance a bit more than the WE bench (figure 7).
- Damping the 20Hz bench resonance by a factor >=3 would reduce the projected noise below the Virgo design, for both the terminal benches.
